Medical imaging and osteoporosis: Fractal's lacunarity analysis of trabecular bone in MR images

The aim of this study was to develop a method of MR image analysis able to provide parameter(s) sensitive to bone microarchitecture changes in aging and osteoporosis onset and progression. The method has been built taking into account fractal properties of many anatomic and physiologic structures. Fractal lacunarity analysis has been used to determine relevant parameter(s) to differentiate among three types of trabecular bone structure (healthy young, healthy perimenopaused, and osteoporotic patients) from lumbar vertebra MR images. In particular, we propose to approximate the lacunarity function by a hyperbola model function, that depends on three different coefficients, alpha, beta, gamma, and to compute these coefficients as the solution of a least squares problem. This tern of cocfficients provides the model function that better represents the variation of mass density of pixels in the image considered. Clinical application of this preliminary version of our method suggests that one of the three coefficients, namely beta, may represent a standard for an evaluation of trabecular bone architecture and a potential useful parametric index in early diagnosis of osteoporosis.